Variables and parameters declaration

While Dynare allows the user to choose their own variable names, there are some restrictions to be kept in mind. First, variables and parameters must not have the same name as Dynare commands or built-in functions. In this respect, Dynare is not case-sensitive. For example, do not use Ln or Sigma_e to name your variable. Not conforming to this rule might yield hard-to-debug error messages or crashes.

var

command

var VAR_NAME [$TEX_NAME$][(long_name=QUOTED_STRINGNAME=QUOTED_STRING)]...;

var (deflator=MODEL_EXPR) VAR_NAME (... same options apply) var(log,deflator=MODEL_EXPR) VAR_NAME (... same options apply)

var (log_deflator=MODEL_EXPR) VAR_NAME (... same options apply)

This required command declares the endogenous variables in the model. Optionally it is possible to give a LaTeX name to the variable or, if it is nonstationary, provide information regarding its deflator. The variables in the list can be separated by spaces or by commas. var commands can appear several times in the file and Dynare will concatenate them.

If the model is nonstationary and is to be written as such in the model block, Dynare will need the trend deflator for the appropriate endogenous variables in order to stationarize the model. The trend deflator must be provided alongside the variables that follow this trend.

Options

log
In addition to the endogenous variable(s) thus declared, this option also triggers the creation of auxiliary variable(s) equal to the log of the corresponding endogenous variable(s). For example, given a var(log) y statement, two endogenous will be created (y and LOG_y), and an auxiliary equation linking the two will also be added (equal to LOG_y = log(y)). Moreover, every occurence of y in the model will be replaced by exp(LOG_y). This option is for example useful when one wants to perform a loglinear approximation of some variable(s) in the context of a first-order stochastic approximation; or when one wants to ensure the variable(s) stay(s) in the definition domain of the function defining the steady state or the dynamic residuals when the nonlinear solver is used.

deflator = MODEL_EXPR
The expression used to detrend an endogenous variable. All trend variables, endogenous variables and parameters referenced in MODEL_EXPR must already have been declared by the trend_var, log_trend_var, var and parameters commands. The deflator is assumed to be multiplicative; for an additive deflator, use log_deflator. This option can be used together with the log option (the latter must come first).

log_deflator = MODEL_EXPR
Same as deflator, except that the deflator is assumed to be additive instead of multiplicative (or, to put it otherwise, the declared variable is equal to the log of a variable with a multiplicative trend). This option cannot be used together with the log option, because it would not make much sense from an economic point of view (the corresponding auxiliary variable would correspond to the log taken two times on a variable with a multiplicative trend).

long_name = QUOTED_STRING
This is the long version of the variable name. Its value is stored in M_.endo_names_long (a column cell array, in the same order as M_.endo_names). In case multiple long_name options are provided, the last one will be used. Default: VAR_NAME.

Example

var c gnp cva 
          cca (long_name=`Consumption CA');
var(deflator=A) i b;
var c $C$ (long_name=`Consumption');

varexo

Command:

 varexo VAR_NAME [$TEX_NAME$] [(long_name=QUOTED_STRING|NAME=QUOTED_STRING)...];

This optional command declares the exogenous variables in the model. Optionally it is possible to give a LaTeX name to the variable. Exogenous variables are required if the user wants to be able to apply shocks to her model. The variables in the list can be separated by spaces or by commas. varexo commands can appear several times in the file and Dynare will concatenate them.

Options

long_name = QUOTED_STRING

Example

    varexo m gov;

Remarks

An exogenous variable is an innovation, in the sense that this
variable cannot be predicted from the knowledge of the current
state of the economy. For instance, if logged TFP is a first order
autoregressive process:
```math
a_t=ρa_{t−1}+ε_t
```

then logged TFP is an endogenous variable to be declared with var, while the innovation ε_t is to be declared with varexo.

varexo_det

Command:

varexo_det VAR_NAME [$TEX_NAME$][(long_name=QUOTED_STRING|NAME=QUOTED_STRING)...];

This optional command declares exogenous deterministic variables in a stochastic model. Optionally it is possible to give a LaTeX name to the variable. The variables in the list can be separated by spaces or by commas. varexo_det commands can appear several times in the file and Dynare will concatenate them.

It is possible to mix deterministic and stochastic shocks to build models where agents know from the start of the simulation about future exogenous changes. In that case stoch_simul will compute the rational expectation solution adding future information to the state space (nothing is shown in the output of stoch_simul) and forecast will compute a simulation conditional on initial conditions and future information.

Note that exogenous deterministic variables cannot appear with a lead or a lag in the model.

Options

long_name = QUOTED_STRING
NAME = QUOTED_STRING

Example

varexo m gov;
varexo_det tau;

parameters

Command:

parameters PARAM_NAME [$TEX_NAME$] [(long_name=QUOTED_STRING|NAME=QUOTED_STRING)...];

This command declares parameters used in the model, in variable
initialization or in shocks declaration. Optionally it is possible to give a
LaTeX name to the parameter.

The parameters must subsequently be assigned values.

The parameters in the list can be separated by spaces or by commas.
``parameters`` commands can appear several times in the file and Dynare
will concatenate them.

Options

long_name = QUOTED_STRING
NAME = QUOTED_STRING

Example

parameters alpha, bet;

Parameter initialization

When using Dynare for computing simulations, it is necessary to calibrate the parameters of the model. This is done through parameter initialization.

The syntax is the following:

PARAMETER_NAME = EXPRESSION;

Here is an example of calibration:

parameters alpha, beta;

beta = 0.99;
alpha = 0.36;
A = 1-alpha*beta;

Internally, the parameter values are stored in context.work.params

Advanced commands

change_type

Command

change_type (var|varexo|varexo_det|parameters) VAR_NAME | PARAM_NAME...;

Changes the types of the specified variables/parameters to another type: endogenous, exogenous, exogenous deterministic or parameter. It is important to understand that this command has a global effect on the $.mod$ file: the type change is effective after, but also before, the $change_type$ command. This command is typically used when flipping some variables for steady state calibration: typically a separate model file is used for calibration, which includes the list of variable declarations with the macro processor, and flips some variable.

Example

var y, w;
parameters alpha, beta;
...
change_type(var) alpha, beta;
change_type(parameters) y, w;

Here, in the whole model file, $alpha$ and $beta$ will be endogenous and $y$ and $w$ will be parameters.

var_remove

Command:

var_remove VAR_NAME | PARAM_NAME...;

Removes the listed variables (or parameters) from the model. Removing a variable that has already been used in a model equation or elsewhere will lead to an error.

predetermined_variables

Command:

predetermined_variables VAR_NAME...;

In Dynare, the default convention is that the timing of a variable reflects when this variable is decided. The typical example is for capital stock: since the capital stock used at current period is actually decided at the previous period, then the capital stock entering the production function is k(-1), and the law of motion of capital must be written:

k = i + (1-delta)*k(-1)

Put another way, for stock variables, the default in Dynare is to use a "stock at the end of the period" concept, instead of a "stock at the beginning of the period" convention.

The predetermined_variables is used to change that convention. The endogenous variables declared as predetermined variables are supposed to be decided one period ahead of all other endogenous variables. For stock variables, they are supposed to follow a "stock at the beginning of the period" convention.

Note that Dynare internally always uses the "stock at the end of the period" concept, even when the model has been entered using the predetermined_variables command. Thus, when plotting, computing or simulating variables, Dynare will follow the convention to use variables that are decided in the current period. For example, when generating impulse response functions for capital, Dynare will plot k, which is the capital stock decided upon by investment today (and which will be used in tomorrow's production function). This is the reason that capital is shown to be moving on impact, because it is k and not the predetermined k(-1) that is displayed. It is important to remember that this also affects simulated time series and output from smoother routines for predetermined variables. Compared to non-predetermined variables they might otherwise appear to be falsely shifted to the future by one period.

Example

The following two program snippets are strictly equivalent.

Using default Dynare timing convention:

var y, k, i;
...
model;
y = k(-1)^alpha;
k = i + (1-delta)*k(-1);
...
end;

Using the alternative timing convention:

var y, k, i;
predetermined_variables k;
...
model;
y = k^alpha;
k(+1) = i + (1-delta)*k;
...
end;

trend_var

command:

trend_var (growth_factor = MODEL_EXPR) VAR_NAME[$LATEX_NAME$]...;

This optional command declares the trend variables in the model. See conv for the syntax of MODEL_EXPR and VAR_NAME. Optionally it is possible to give a LaTeX name to the variable.

The variable is assumed to have a multiplicative growth trend. For an additive growth trend, use log_trend_var instead.

Trend variables are required if the user wants to be able to write a nonstationary model in the model block. The trend_var command must appear before the var command that references the trend variable.

trend_var commands can appear several times in the file and Dynare will concatenate them.

If the model is nonstationary and is to be written as such in the model block, Dynare will need the growth factor of every trend variable in order to stationarize the model. The growth factor must be provided within the declaration of the trend variable, using the growth_factor keyword. All endogenous variables and parameters referenced in MODEL_EXPR must already have been declared by the var and parameters commands.

Example

trend_var (growth_factor=gA) A;

make_local_variables

command:

model_local_variable VARIABLE_NAME [LATEX_NAME]... ;

This optional command declares a model local variable. See conv for the syntax of VARIABLE_NAME. As you can create model local variables on the fly in the model block, the interest of this command is primarily to assign a LATEX_NAME to the model local variable.

Example

model_local_variable GDP_US $GDPUS$;

On-the-fly Model Variable Declaration

Endogenous variables, exogenous variables, and parameters can also be declared inside the model block. You can do this in two different ways: either via the equation tag or directly in an equation.

To declare a variable on-the-fly in an equation tag, simply state the type of variable to be declared (endogenous, exogenous, or parameter followed by an equal sign and the variable name in single quotes. Hence, to declare a variable c as endogenous in an equation tag, you can type [endogenous='c'].

To perform on-the-fly variable declaration in an equation, simply follow the symbol name with a vertical line (|, pipe character) and either an e, an x, or a p. For example, to declare a parameter named alphaa in the model block, you could write alphaa|p directly in an equation where it appears. Similarly, to declare an endogenous variable c in the model block you could write c|e. Note that in-equation on-the-fly variable declarations must be made on contemporaneous variables.

On-the-fly variable declarations do not have to appear in the first place where this variable is encountered.

Example

The following two snippets are equivalent:

model;
  [endogenous='k',name='law of motion of capital']
  k(+1) = i|e + (1-delta|p)*k;
  y|e = k^alpha|p;
  ...
end;
delta = 0.025;
alpha = 0.36;

var k, i, y;
parameters delta, alpha;
delta = 0.025;
alpha = 0.36;
...
model;
  [name='law of motion of capital']
  k(1) = i|e + (1-delta|p)*k;
  y|e = k|e^alpha|p;
  ...
end;